User:PAR
Image:Original_Barnstar.png ]]
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Subjects I'm working on
{{note_label|Wood1992||}}
- References
{{note_label|Wood1992||}} {{ref_harvard|Wood1992|Wood, 1992|}} - References
reference,, ,{{rp|p.103}} - References (Harvard with pages)
- Template:Cite_web
- Template:Cite_journal
- Template:cite book{{cite journal |last1=Herrmann |first1=F. |last2=Würfel |first2=P.|year=2005 |title=Light with nonzero chemical potential |journal=Am. J. Phys |volume=78 |issue=3 |pages=717-721 |publisher=American Association of Physics Teachers |doi=10.1119/1.1904623 |url=https://www.google.com/#hl=en&tbo=d&sclient=psy-ab&q=Herrmann+%22Light+with+nonzero+chemical+potential%22&oq=Herrmann+%22Light+with+nonzero+chemical+potential%22&gs_l=hp.3...227562.227562.1.228017.1.1.0.0.0.0.0.0..0.0.les%3Bcpsugrpq2high..0.0...1.vSu9w3P37vw&pbx=1&bav=on.2,or.r_gc.r_pw.r_qf.&bvm=bv.1355534169,d.eWU&fp=5d1955e51bd5f1c6&bpcl=40096503&biw=1638&bih=807 |accessdate=2012-12-20}} A necessary condition for Planck's law to hold is that the photon number is not conserved, implying that the chemical potential of the photons is zero. While this may be unavoidably true on very long timescales, there are many practical cases that are dealt with by assuming a nonzero chemical potential, which yields an equilibrium distribution which is not Planckian.
- History of Wayne, NY
- Australian Trilobite Jump table
- RGB
- -
- Pigment-loss color blindness
- Peach
- Work7
- Work8
- Extension to Kummer's test
- Work10
- Elastic Moduli
- Work 12
- Principle of maximum entropy
- Principle of maximum work
- Principle of minimum energy
- Minimum total potential energy principle
- Template talk:probability distribution#Status of usage
- Template talk:Prettytable and MediaWiki talk:Common.css
- verify μ is mode of Levy distribution
- Combine Heavy tail distribution and Long tail
- Mutation-selection balance | Quasispecies model | http://www.biomedcentral.com/1471-2148/5/44
[[Thermodynamics]]
Chi-squared distributions
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|+ |distribution | | |
scale-inverse-chi-squared distribution
| | |
inverse-chi-squared distribution 1
| | |
inverse-chi-squared distribution 2
| | |
inverse gamma distribution
| | |
Levy distribution
| | |
Heavy tail distributions
Heavy tail distributions
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Distribution
|character | |
Levy skew alpha-stable distribution
|continuous, stable | |
Cauchy distribution
|continuous, stable | |
Voigt distribution
|continuous | |
Levy distribution
|continuous, stable | |
scale-inverse-chi-squared distribution
|continuous | |
inverse-chi-squared distribution
|continuous | |
inverse gamma distribution
|continuous | |
Pareto distribution
|continuous | |
Zipf's law
|discrete | |
Zipf-Mandelbrot law
|discrete | |
Zeta distribution
|discrete | |
Student's t-distribution
|continuous | |
Yule-Simon distribution
|discrete | |
? distribution
|continuous | |
Log-normal distribution???
|continuous | |
Weibull distribution???
|? | |
Gamma-exponential distribution???
|? | |
[[Statistical Mechanics]]
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|+ A Table of Statistical Mechanics Articles |
align="center" |
! align="center" |Maxwell Boltzmann ! align="center" |Bose-Einstein ! align="center" |Fermi-Dirac |
---|
align="center" |Particle
| align="center" | | align="center" |Boson | align="center" |Fermion |
align="center" |Statistics
| align="center" colspan=3 | Identical particles#Statistical properties Statistical ensemble|Microcanonical ensemble | Canonical ensemble | Grand canonical ensemble |
align="center" |Statistics
| align="center" | Maxwell-Boltzmann distribution Derivation of the partition function | align="center" |Bose-Einstein statistics | align="center" |Fermi-Dirac statistics |
align="center" | Thomas-Fermi approximation | align="center" colspan=3 | gas in a box |
align="center" |Gas
| align="center" |Ideal gas | align="center" | Planck's law of black body radiation | align="center" | |
align="center" | Chemical Equilibrium | align="center" | Classical Chemical equilibrium | align="center" colspan=2| |
Others:
Continuum mechanics
- http://online.physics.uiuc.edu/courses/phys598OS/fall04/lectures/
Work pages
To fix:
- Degenerate distribution
- Fermi-Dirac statistics - not continuous, necessarily
- Bose gas (derive critical temperature)
- Spectral density-SPD Cat:Physics = Power spectrum-Cat:signal processing
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(subtract mean)
|(no subtract mean) |
Covariance |
Cross covariance
|Cross correlation see [http://astronomy.swin.edu.au/~pbourke/analysis/correlate/ ext] |
Autocovariance |
Covariance matrix |
Estimation of covariance matrices |
Proof: Introduce an additional heat reservoir at an arbitrary temperature T0, as well as N cycles with the following property: the j-th such cycle operates between the T0 reservoir and the Tj reservoir, transferring energy dQj to the latter. From the above definition of temperature, the energy extracted from the T0 reservoir by the j-th cycle is
:
Now consider one cycle of the heat engine, accompanied by one cycle of each of the smaller cycles. At the end of this process, each of the N reservoirs have zero net energy loss (since the energy extracted by the engine is replaced by the smaller cycles), and the heat engine has done an amount of work equal to the energy extracted from the T0 reservoir,
:
If this quantity is positive, this process would be a perpetual motion machine of the second kind, which is impossible. Thus,
:
Now repeat the above argument for the reverse cycle. The result is
: (reversible cycles)
In mathematics, it is often desireable to express a functional relationship as a different function, whose argument is the derivative of f , rather than x . If we let y=df/dx be the argument of this new function, then this new function is written and is called the Legendre transform of the original function.
- Random variable
- Random sequence
- Random number
- Pseudorandom number generator
- STOCHASTIC PROCESS
- Time series
- Stationary process
- :Category:Random numbers
- :Category:Stochastic processes
- :Category:Noise
- :Category:Statistics
- :Category:Probability theory
Category:Wikipedians interested in thermodynamics
References
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|colspan="3" style="text-align: center;"|Wall (Impermeable) | |||||||||||
Rigid | T-Ins | No IW | External | ||||||||
δQh | δWx | dT | dS | dP | dV | dN | dV=0 | δQh=0 | δWx=0 | ||
Process | |||||||||||
Isobaric process | | |||||||||||
|0 | | |||||||||||
|0 | no | | ||||||||||
|constant pressure reservoir | |||||||||||
Isochoric process| | |||||||||||
|0 | 0 | | ||||||||||
|yes | | |||||||||||
Isothermal process| | |||||||||||
|0 | | |||||||||||
|0 | | |||||||||||
|no | | |||||||||||
|constant temperature reservoir | |||||||||||
Isentropic process | 0 | 0 | | |||||||||
|0 | | |||||||||||
|0 | | |||||||||||
|yes | yes | | ||||||||||
Adiabatic process | 0 | | ||||||||||
|0 | | |||||||||||
|yes | | |||||||||||
x-Isolated System | |||||||||||
Mechanically Is. (Guha) | | |||||||||||
|0 | 0 | yes | | |||||||||
Adiabatic Is | 0 | | ||||||||||
|0 | | |||||||||||
|yes | | |||||||||||
Thermally Is. | 0 | 0 | | |||||||||
|0 | | |||||||||||
|0 | | |||||||||||
|yes | yes | | ||||||||||
Closed system | | |||||||||||
|0 | | |||||||||||
Isolated system | 0 | 0 | | |||||||||
|0 | | |||||||||||
|0 | 0 | yes | yes | yes | | |||||||
Open system | | |||||||||||
|no | no | no | | |||||||||
Conserved Thermodynamic potential | |||||||||||
U: Internal energy | 0 | 0 | | |||||||||
|0 | | |||||||||||
|0 | 0 | yes | yes | yes | | |||||||
F: Helmholtz free energy | | |||||||||||
|0 | | |||||||||||
|0 | 0 | yes | no | | ||||||||
|constant temperature reservoir | |||||||||||
H: Enthalpy | 0 | 0 | | |||||||||
|0 | 0 | | ||||||||||
|0 | no | yes | yes | constant pressure reservoir | |||||||
G: Gibbs free energy | | |||||||||||
|0 | | |||||||||||
|0 | | |||||||||||
|0 | no | no | | |||||||||
|constant pressure and temperature reservoir |
δQh is heat, δWx is irreversible work, so TdS=δQh+δWx. If both are zero, then dS=0. For the 3 possible walls, "T ins" means thermally insulated, and "No IW" means no irreversible work. "External" specifies the region external to the system.